Q I have bought a new iMac, and now want to clean up my old one. I want to merge its two partitions into one, and provide it with a fresh installation of El Capitan. I have tried to do this, but cannot even get it to start up properly in Recovery mode. What should I do?
A Recovery mode (Command-R at startup) should give access to this, but you must have the iMac connected to the Internet, and it is often best with a wired keyboard and mouse. This is detailed here.
When the iMac starts up from its recovery partition and the Internet, you should then engage Disk Utility to change the drive’s partitioning. Select the disk (rather than either volume) and the Partition tool, following which you should install El Capitan.
If you cannot get it to do this in Recovery mode, then the next plan is to start it up from a bootable install USB memory stick (at least 8 GB in size). Instructions for creating such a stick are given on Ars Technica. The easy route is to use DiskMaker X (donationware), which will set up the USB stick.
However, as your iMac is new, DiskMaker may well be unable to find a suitable installable copy of El Capitan. The simplest way to acquire that is to download it from the Mac App Store, although at slightly more than 6 GB that could take a while. DiskMaker should then be able to install that on the USB stick, you can then start your old iMac from that stick, repartition the drive using Disk Utility, and install a fresh copy of El Capitan.